Re: Inverse error function for arguments close to 1
- To: mathgroup at smc.vnet.net
- Subject: [mg12675] Re: [mg12653] Inverse error function for arguments close to 1
- From: Wouter Meeussen <eu000949 at pophost.eunet.be>
- Date: Mon, 1 Jun 1998 23:16:48 -0400
- Sender: owner-wri-mathgroup at wolfram.com
hi Jacek, I see only two ways: 1/ Use InverseErfc[arg] for arguments close to 0 : In[31]:= Table[N at InverseErf[1-Exp[-x]],{x,0,50}] Out[31]= {0,0.636716,1.05599,1.38719,1.66819,1.91592,2.13965,2.34504,2.53586,2.71476, 2.88367,3.04407,3.19709,3.34365,3.48449,3.62023,3.75136,3.87832,4.00148, 4.12116,4.23763,4.35113,4.46188,4.57006,4.67585,4.77939,4.88081,4.98025, 5.07782,5.17361,5.26769,5.36024,5.45126,5.54067,5.63142,5.711,5.80502, 5.86358,\[Infinity],\[Infinity],\[Infinity],\[Infinity],\[Infinity], \[Infinity],\[Infinity],\[Infinity],\[Infinity],\[Infinity],\[Infinity], \[Infinity],\[Infinity]} In[32]:= Table[N at InverseErfc[ Exp[-x]],{x,0,50}] Out[32]= {0.,0.636716,1.05599,1.38719,1.66819,1.91592,2.13965,2.34504,2.53586,2.71476, 2.88367,3.04407,3.19709,3.34365,3.48449,3.62023,3.75136,3.87832,4.00148, 4.12116,4.23763,4.35113,4.46188,4.57006,4.67585,4.77938,4.88081,4.98025, 5.07782,5.1736,5.26771,5.36022,5.4512,5.54074,5.6289,5.71574,5.80131, 5.88567,5.96888,6.05097,6.13198,6.21197,6.29097,6.369,6.44612,6.52234, 6.59771,6.67224,6.74596,6.8189,6.89109} 2/ Use "high precision" in stead of machine precision (one of Mathematica strong points!) In[26]:= Table[{N[InverseErf[1-Exp[-x]],18], N[InverseErfc[Exp[-x]],18]},{x,50,60}] Out[26]= {{6.8910913629004655,6.8910913629004660}, {6.9625447358489660,6.9625447358489663}, {7.0332863431220254,7.0332863431220248}, {7.1033369139523046,7.1033369139523048}, ... enjoy, wouter. At 17:36 30-05-98 -0400, Jacek Pliszka wrote: >Hi! > >I need to calculate: > >InverseErf[1-Exp[-x]] for x \approx 50. > >I am trying to use mathematica but it doesn't work for such a large >values. > >Does anybody know how to solve that? Where to look for the proper >approximation? > >I've looked through a few textbooks but I didn't find an answer. The >only solution I have now is numerical solution of the equation >Erf[z]+Exp[-x]=1 with high precision calculation for each integral >needed for iteration step. > >Regards, > >Jacek Pliszka > >Tmp: pliszka at bethe.ucdavis.edu Perm: pliszka at fuw.edu.pl > > > Dr. Wouter L. J. MEEUSSEN w.meeussen.vdmcc at vandemoortele.be eu000949 at pophost.eunet.be